# sJIVE: Supervised Joint and Individual Variation Explained

arXiv: https://arxiv.org/abs/2102.13278 · HTML: https://mlsanity.com/paper/2102.13278/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 26 Feb 2021.

## Builds on (most cited first, 11 of 11)

- [Angle-Based Joint and Individual Variation Explained](https://mlsanity.com/paper/1704.02060/) (2017)
- [Structural Learning and Integrative Decomposition of Multi-View Data](https://mlsanity.com/paper/1707.06573/) (2017)
- [Collaborative Regression](https://mlsanity.com/paper/1401.5823/) (2014)
- [Sparse Linear Discriminant Analysis for Multi-view Structured Data](https://mlsanity.com/paper/1911.05643/) (2019)
- [Joint association and classification analysis of multi-view data](https://mlsanity.com/paper/1811.08511/) (2018)
- [Bayesian Integrative Analysis and Prediction with Application to Atherosclerosis Cardiovascular Disease](https://mlsanity.com/paper/2005.11586/) (2020)
- [Generalized Integrative Principal Component Analysis for Multi-Type Data with Block-Wise Missing Structure](https://mlsanity.com/paper/1808.02193/) (2018)
- [Sparse canonical correlation analysis from a predictive point of view](https://mlsanity.com/paper/1501.01231/) (2015)
- [Robust Sparse Canonical Correlation Analysis](https://mlsanity.com/paper/1501.01233/) (2015)
- [Incorporating Covariates into Integrated Factor Analysis of Multi-View Data](https://mlsanity.com/paper/1703.05794/) (2017)
- [FDR-Corrected Sparse Canonical Correlation Analysis with Applications to Imaging Genomics](https://mlsanity.com/paper/1705.04312/) (2017)

## Built on by (most cited first, 15 of 15)

- [Optimal Estimation of Shared Singular Subspaces across Multiple Noisy Matrices](https://mlsanity.com/paper/2411.17054/) (2024)
- [Bayesian Joint Additive Factor Models for Multiview Learning](https://mlsanity.com/paper/2406.00778/) (2024)
- [A spectral method for multi-view subspace learning using the product of projections](https://mlsanity.com/paper/2410.19125/) (2024)
- [Bayesian Simultaneous Factorization and Prediction Using Multi-Omic Data](https://mlsanity.com/paper/2211.16403/) (2022)
- [Scalable Randomized Kernel Methods for Multiview Data Integration and Prediction](https://mlsanity.com/paper/2304.04692/) (2023)
- [Learning Joint and Individual Structure in Network Data with Covariates](https://mlsanity.com/paper/2406.08776/) (2024)
- [Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Data](https://mlsanity.com/paper/2505.24413/) (2025)
- [Inference on covariance structure in high-dimensional multi-view data](https://mlsanity.com/paper/2509.02772/) (2025)
- [Bayesian predictive modeling of multi-source multi-way data](https://mlsanity.com/paper/2208.03396/) (2022)
- [mvlearnR and Shiny App for multiview learning](https://mlsanity.com/paper/2311.16181/) (2023)
- [A deep learning pipeline for cross-sectional and longitudinal multiview data integration](https://mlsanity.com/paper/2312.01238/) (2023)
- [Multiple Linked Tensor Factorization](https://mlsanity.com/paper/2502.20286/) (2025)
- [Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAS](https://mlsanity.com/paper/2607.18209/) (2026)
- [The Trade-off Between Covariate Dependence and Latent Structure in Representation Learning](https://mlsanity.com/paper/2608.16245/) (2026)
- [Structured Latent Modeling for Supervised Multimodal Information Decomposition](https://mlsanity.com/paper/2609.35502/) (2026)

## Abstract (arXiv)

Analyzing multi-source data, which are multiple views of data on the same subjects, has become increasingly common in molecular biomedical research. Recent methods have sought to uncover underlying structure and relationships within and/or between the data sources, and other methods have sought to build a predictive model for an outcome using all sources. However, existing methods that do both are presently limited because they either (1) only consider data structure shared by all datasets while ignoring structures unique to each source, or (2) they extract underlying structures first without consideration to the outcome. We propose a method called supervised joint and individual variation explained (sJIVE) that can simultaneously (1) identify shared (joint) and source-specific (individual) underlying structure and (2) build a linear prediction model for an outcome using these structures. These two components are weighted to compromise between explaining variation in the multi-source data and in the outcome. Simulations show sJIVE to outperform existing methods when large amounts of noise are present in the multi-source data. An application to data from the COPDGene study reveals gene expression and proteomic patterns that are predictive of lung function. Functions to perform sJIVE are included in the R.JIVE package, available online at http://github.com/lockEF/r.jive .